Generally, one can attempt to mitigate errors in the whole computation at different levels, such as at the level of gates [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, circuits [7]}, [8]}, [9]}, full QECCs [10]}, or even entire algorithms [11]}, [12]}. Recent work [13]} has described how to combat crosstalk in ion traps on the level of QECCs and circuits by choosing the arrangement of qubits in the QECC circuitry to minimise the fault-tolerant breaking effects of crosstalk, and by comparing the performance of different QECCs in the compass-code QEC family. As a complementary approach, we will investigate a technique that suppresses crosstalk directly at the gate level. Gate-level mitigation of noise can suppress and change the nature of any remaining effective noise. Thus, one may want to consider such techniques when evaluating the performance and merits of different QEC protocols. In particular, we will concentrate on a flag-based scheme [9]} for the distance-three seven-qubit colour code. Our purpose is to analyse whether the refocussing technique, to be described in detail below, allows this QEC-operated logical qubit to outperform a physical qubit in the presence of microscopic errors that include crosstalk. Here, we want to identify the specific regimes where this QEC advantage becomes possible, informing future hardware improvements. We will also explore the consequences of the coherent nature of crosstalk and the extent to which it is possible to suppress its impact on QEC. We consider near-term noise rates and crosstalk, building on previous works [15]}, and extend the noise models towards a more complete description. It should be noted that although our study focuses on a trapped-ion quantum processor and the example of the 7-qubit colour code, the error mitigation technique and analysis discussed here can be adapted to other quantum processor architectures, or other QECCs and algorithms.
